.help aop Jun99 "Slalib Package"
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      SUBROUTINE slAOP (RAP, DAP, DATE, DUT, ELONGM, PHIM, HM,
     :                    XP, YP, TDK, PMB, RH, WL, TLR,
     :                    AOB, ZOB, HOB, DOB, ROB)

     - - - -
      A O P
     - - - -

  Apparent to observed place, for optical sources distant from
  the solar system.

  Given:
     RAP    d      geocentric apparent right ascension
     DAP    d      geocentric apparent declination
     DATE   d      UTC date/time (Modified Julian Date, JD-2400000.5)
     DUT    d      delta UT:  UT1-UTC (UTC seconds)
     ELONGM d      mean longitude of the observer (radians, east +ve)
     PHIM   d      mean geodetic latitude of the observer (radians)
     HM     d      observer's height above sea level (metres)
     XP     d      polar motion x-coordinate (radians)
     YP     d      polar motion y-coordinate (radians)
     TDK    d      local ambient temperature (DegK; std=273.155D0)
     PMB    d      local atmospheric pressure (mB; std=1013.25D0)
     RH     d      local relative humidity (in the range 0D0-1D0)
     WL     d      effective wavelength (micron, e.g. 0.55D0)
     TLR    d      tropospheric lapse rate (DegK/metre, e.g. 0.0065D0)

  Returned:
     AOB    d      observed azimuth (radians: N=0,E=90)
     ZOB    d      observed zenith distance (radians)
     HOB    d      observed Hour Angle (radians)
     DOB    d      observed Declination (radians)
     ROB    d      observed Right Ascension (radians)

  Notes:

   1)  This routine returns zenith distance rather than elevation
       in order to reflect the fact that no allowance is made for
       depression of the horizon.

   2)  The accuracy of the result is limited by the corrections for
       refraction.  Providing the meteorological parameters are
       known accurately and there are no gross local effects, the
       predicted apparent RA,Dec should be within about 0.1 arcsec
       for a zenith distance of less than 70 degrees.  Even at a
       topocentric zenith distance of 90 degrees, the accuracy in
       elevation should be better than 1 arcmin;  useful results
       are available for a further 3 degrees, beyond which the
       slRFRO routine returns a fixed value of the refraction.
       The complementary routines slAOP (or slAOPQ) and slOAP
       (or slOAPQ) are self-consistent to better than 1 micro-
       arcsecond all over the celestial sphere.

   3)  It is advisable to take great care with units, as even
       unlikely values of the input parameters are accepted and
       processed in accordance with the models used.

   4)  "Apparent" place means the geocentric apparent right ascension
       and declination, which is obtained from a catalogue mean place
       by allowing for space motion, parallax, precession, nutation,
       annual aberration, and the Sun's gravitational lens effect.  For
       star positions in the FK5 system (i.e. J2000), these effects can
       be applied by means of the slMAP etc routines.  Starting from
       other mean place systems, additional transformations will be
       needed;  for example, FK4 (i.e. B1950) mean places would first
       have to be converted to FK5, which can be done with the
       slFK45 etc routines.

   5)  "Observed" Az,El means the position that would be seen by a
       perfect theodolite located at the observer.  This is obtained
       from the geocentric apparent RA,Dec by allowing for Earth
       orientation and diurnal aberration, rotating from equator
       to horizon coordinates, and then adjusting for refraction.
       The HA,Dec is obtained by rotating back into equatorial
       coordinates, using the geodetic latitude corrected for polar
       motion, and is the position that would be seen by a perfect
       equatorial located at the observer and with its polar axis
       aligned to the Earth's axis of rotation (n.b. not to the
       refracted pole).  Finally, the RA is obtained by subtracting
       the HA from the local apparent ST.

   6)  To predict the required setting of a real telescope, the
       observed place produced by this routine would have to be
       adjusted for the tilt of the azimuth or polar axis of the
       mounting (with appropriate corrections for mount flexures),
       for non-perpendicularity between the mounting axes, for the
       position of the rotator axis and the pointing axis relative
       to it, for tube flexure, for gear and encoder errors, and
       finally for encoder zero points.  Some telescopes would, of
       course, exhibit other properties which would need to be
       accounted for at the appropriate point in the sequence.

   7)  This routine takes time to execute, due mainly to the
       rigorous integration used to evaluate the refraction.
       For processing multiple stars for one location and time,
       call slAOPA once followed by one call per star to slAOPQ.
       Where a range of times within a limited period of a few hours
       is involved, and the highest precision is not required, call
       slAOPA once, followed by a call to slAOPT each time the
       time changes, followed by one call per star to slAOPQ.

   8)  The DATE argument is UTC expressed as an MJD.  This is,
       strictly speaking, wrong, because of leap seconds.  However,
       as long as the delta UT and the UTC are consistent there
       are no difficulties, except during a leap second.  In this
       case, the start of the 61st second of the final minute should
       begin a new MJD day and the old pre-leap delta UT should
       continue to be used.  As the 61st second completes, the MJD
       should revert to the start of the day as, simultaneously,
       the delta UTC changes by one second to its post-leap new value.

   9)  The delta UT (UT1-UTC) is tabulated in IERS circulars and
       elsewhere.  It increases by exactly one second at the end of
       each UTC leap second, introduced in order to keep delta UT
       within +/- 0.9 seconds.

  10)  IMPORTANT -- TAKE CARE WITH THE LONGITUDE SIGN CONVENTION.
       The longitude required by the present routine is east-positive,
       in accordance with geographical convention (and right-handed).
       In particular, note that the longitudes returned by the
       slOBS routine are west-positive, following astronomical
       usage, and must be reversed in sign before use in the present
       routine.

  11)  The polar coordinates XP,YP can be obtained from IERS
       circulars and equivalent publications.  The maximum amplitude
       is about 0.3 arcseconds.  If XP,YP values are unavailable,
       use XP=YP=0D0.  See page B60 of the 1988 Astronomical Almanac
       for a definition of the two angles.

  12)  The height above sea level of the observing station, HM,
       can be obtained from the Astronomical Almanac (Section J
       in the 1988 edition), or via the routine slOBS.  If P,
       the pressure in millibars, is available, an adequate
       estimate of HM can be obtained from the expression

             HM ~ -29.3D0*TSL*LOG(P/1013.25D0).

       where TSL is the approximate sea-level air temperature in
       deg K (see Astrophysical Quantities, C.W.Allen, 3rd edition,
       section 52.)  Similarly, if the pressure P is not known,
       it can be estimated from the height of the observing
       station, HM as follows:

             P ~ 1013.25D0*EXP(-HM/(29.3D0*TSL)).

       Note, however, that the refraction is proportional to the
       pressure and that an accurate P value is important for
       precise work.

  13)  The azimuths etc produced by the present routine are with
       respect to the celestial pole.  Corrections to the terrestrial
       pole can be computed using slPLMO.

  Called:  slAOPA, slAOPQ

  P.T.Wallace   Starlink   9 June 1998

  Copyright (C) 1998 Rutherford Appleton Laboratory
  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.

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